Length Formulas for the Local Cohomology of Exterior Powers.
Local Cohomolgy Along Exceptional Sets.
Local cohomology and support for triangulated categories
We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Special cases are, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of...
Local cohomology and the connectedness dimension in algebraic varieties.
Local Cohomology and the Cousin Complex for a Commutative Noetherian Ring.
Local cohomology, cofiniteness and homological functors of modules
Let be an ideal of a commutative Noetherian ring . It is shown that the -modules are -cofinite for all finitely generated -modules and all if and only if the -modules and are -cofinite for all finitely generated -modules , and all integers .
Local cohomology multiplicities in terms of étale cohomology
Using a recently introduced correspondence of Emerton-Kisin we give a description of Lyubeznik’s local cohomology invariants in terms of local étale cohomology with coefficients.
Local homology and cohomology on schemes
Local volumes of Cartier divisors over normal algebraic varieties
In this paper we study a notion of local volume for Cartier divisors on arbitrary blow-ups of normal complex algebraic varieties of dimension greater than one, with a distinguished point. We apply this to study an invariant for normal isolated singularities, generalizing a volume defined by J. Wahl for surfaces. We also compare this generalization to a different one arising in recent work of T. de Fernex, S. Boucksom, and C. Favre.
Lokale Algebra und lokale Geometrie.